Feedback control: Two-sided Markov-modulated Brownian motion with instantaneous change of phase at boundaries

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• 作者：Guy Latouche^a ; ^{latouche@ulb.ac.be}Author Vitae ; Giang T. Nguyen^b ; ^{giang.nguyen@adelaide.edu.au}Author Vitae
• 关键词：Fluid queues ; Markov-modulated Brownian motion ; Regenerative processes ; Finite buffer ; Stationary distribution ; Feedback
• 刊名：Performance Evaluation
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：106
• 期：Complete
• 页码：30-49
• 全文大小：681 K
• 卷排序：106

文摘

We consider a Markov-modulated Brownian motion {Y(t),ρ(t)}{Y(t),ρ(t)} with two boundaries at 00 and b>0b>0, and allow for the controlling Markov chain {ρ(t)}{ρ(t)} to instantaneously undergo a change of phase upon hitting either of the two boundaries at semi-regenerative epochs defined to be the first time the process reaches a boundary since it last hits the other boundary. We call this process a flexible Markov-modulated Brownian motion.Using the recently-established links between stochastic fluid models and Markov-modulated Brownian motions, we determine important characteristics of first exit times of a Markov-modulated Brownian motion from an interval with a regulated boundary. These results allow us to follow a Markov-regenerative approach and obtain the stationary distribution of the flexible process. This highlights the effectiveness of the regenerative approach in analyzing Markov-modulated Brownian motions subject to more general boundary behaviors than the classic regulated boundaries.